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math question 1 week 7

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many type of solutions?
Please provide the name for each type of solution.
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1 Answer

Type of solution of quadratic depends on the value of Discriminant:  b^2 - 4ac
  Roots are evaluated by factoring the equation of 
   aX^2 + bx + c
  a ( X - b/ 2a ) ^2 - ( b^2 - 4ac)/ 4a^2  
   X1 , X = -b/2a ±√(b^2 - 4ac) /2a
     if   b^2 - 4ac > 0  , then quadratic has 2 real roos
               a.  b^2 -4ac is a perfect square then the roots are rational
               b . b^2 - 4ac not a perfect square, then the roots are irrational
    if  b^2 - 4ac< 0 , then quadratic has 2 complex roots.
      Quadratic always has 2 roots.
         The irrational and complex roots has to appear as conjugate pair for the coefficients of the quadratic
          to be integers.
                X = a ± bi 
                 X = a ± √b